Question: Simplify the expression. $(4k^{4}-2k^{2})(4k^{3}+2k^{2}+4k)$
Solution: First use the distributive property. $ 4 k^4 (4 k^3) + 4 k^4 (2 k^2) + 4 k^4 (4 k) - 2 k^2 (4 k^3) - 2 k^2 (2 k^2) - 2 k^2 (4 k) $ Simplify. $ 16k^{7} + 8k^{6} + 16k^{5} - 8k^{5} - 4k^{4} - 8k^{3} $ $16k^{7}+8k^{6}+8k^{5}-4k^{4}-8k^{3}$ Identify like terms. $ { 16k^{7}} {+ 8k^{6}} {+ 16k^{5}} {- 8k^{5}} {- 4k^{4}} {- 8k^{3}} $ Add the coefficients. $ { 16k^{7}} {+ 8k^{6}} {+ 8k^{5}} { -4k^{4}} { -8k^{3}} $